We return to a simple model of DNA-transcription, first investigated by Salerno more than 10 years ago. One conjecture that time was that the promoter-regions were "dynamically active" in the sense that a stationary kink solution to the discrete sine-Gordon equation spontaneously starts to move when positioned in certain regions. Here we explore the whole genome of the bacteriophage T7, which is the same that was used in the first studies. We find that the regions in the promoters where the DNA-binding molecules attach have no special significance, while the start of the RNA-coding regions are dynamically active on a significant level. The results are checked to be robust by imposing an external disturbance in the form of a thermostat, simulating a constant temperature. © 2002 Elsevier Science B.V. All rights reserved.

The question of localization in a one-dimensional tight-binding model with aperiodicity given by substitutions is discussed. Since the localization properties of the well-known Rudin-Shapiro chain is still far from well understood, partly due to the absence of rigorous analytical results, we introduce a sequence that has several features in common with the Rudin-Shapiro sequence. We derive a trace map for this system and prove analytically that the electron spectrum is singular continuous. Despite the extended (non-normalizable) nature of the corresponding wave functions, the states show strong localization for finite approximations of the chain. Similar localization properties are found for the Rudin-Shapiro chain, where earlier results have indicated a pure point spectrum. We compare the properties for two other physical systems, ordered according to the two discussed sequences; stationary electron transmission is studied through finite chains using a dynamical map, optical properties of dielectric multilayer structures are investigated.

This study presents various aspects of discrete breathers in diatomic FPU lattices with masses varying according to the aperiodic Fibonacci and Thue-Morse sequences. We investigate the existence of time-periodic breathers, starting from the anti-continuous limit and consider excitations of isolated light atoms, hence obtaining the domain of unique existence for these breathers. We also perform a linear stability analysis by studying the Floquet operator. The found exact solutions are used, slightly perturbed, as initial conditions for long-time simulations of the breathers. These breathers turn out to be robust. Finally we consider how initial excitations of two consecutive light atoms evolve. Depending on the properties of the phase space for the two-atom system at the anti-continuous limit, we obtain different behaviour of these excitations. Especially we find that the aperiodic lattices can support localized excitations with a continuous frequency distribution for the timescales we consider, while a periodic lattice is unable to. These excitations are referred to as chaotic breathers. (C)2000 Elsevier Science B.V. All rights reserved.

Effects of the combination of nonlinearities and aperiodic order is studied in this thesis. The nonlinear systems considered are Josephson junction arrays (JJA) and Fermi-Pasta-Ulam (FPU) lattices. Both systems are discrete and one-dimensional. The traveling waves in a JJA are solitons, i.e., coherent structures which retain their shape and speed as they propagate. The properties of both these system is influenced by the ordering of their respective constituents. In the thesis some aperiodicaly orderd structures are described, including some typical effects on systems which are aper iodically orderd. Next, a description of Josephson junctions are given and also some physical features for system sconsisting of these junctions. A number of practical applications are given, Finally discrete breathers are described, including existence conditions and some possible applications.

Paper 1: Fluxon propagation in discrete Josepson junction arrays is examined. Sometimes a fluxon can be pinned in the array and we derive an effective potential which can explain why this happens, and predict at which positions a fluxon can get pinned.

Paper2; Discrete breathers are shown to exist in aperiodically ordered, diatomic FPU lattices. Localized modes survives for longer times in Fibonacci and Thue-Morse lattices compared to a periodic lattice. The conjecture is that the gaps in the linear phonon spectrum of the aperiodically orderd structures hinder resonances with the linear spectrum.leading to the longer life times.

Paper 3: Moving breathers in FPU lattices are examined. These have frequencies in the linear bands. Interaction with noise and imourity atoms are further considered.

Paper 4: Current-voltage (I-V) curves are calculated for Josephson junction arrays, which consist of two different types of junctions. A monoarray is compared to a periodic array and a Fibonacci array. There are marked differences in the I-V curves for these systems. New states with kink a structure superimposed on the rotating McCumber background are found in periodic array and in the Fibonacci array.